Scales, fields, and a problem of Hurewicz

Details Scales, fields, and a problem of Hurewicz Scales, fields, and a problem of Hurewicz

2005-07-03

arxiv.org/abs/math/0507043v6

Journal of the European Mathematical Society 10 (2008), 837-866

Mathematics

General Topology

Scientific paper

10.4171/JEMS/132

Menger's basis property is a generalization of $\sigma$-compactness and admits an elegant combinatorial interpretation. We introduce a general combinatorial method to construct non $\sigma$-compact sets of reals with Menger's property. Special instances of these constructions give known counterexamples to conjectures of Menger and Hurewicz. We obtain the first explicit solution to the Hurewicz 1927 problem, that was previously solved by Chaber and Pol on a dichotomic basis. The constructed sets generate nontrivial subfields of the real line with strong combinatorial properties, and most of our results can be stated in a Ramsey-theoretic manner. Since we believe that this paper is of interest to a diverse mathematical audience, we have made a special effort to make it self-contained and accessible.

Affiliated with

Also associated with

No associations

Rating

Scales, fields, and a problem of Hurewicz does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Scales, fields, and a problem of Hurewicz, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scales, fields, and a problem of Hurewicz will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-209284